"I will be interested to see if any specimens of his handwriting survive from his admissions to workhouses and asylums which might compare to any of the notes written to the police. "
The notes have long been considered a hoax - very few people belive any of them were genuinely written by the killer.
Overall, we can't claim this as fact yet, because these people have not published their exact methodology - we know they had samples of DNA from both Kosminski and Eddowes in the same lab, and it is entirely possible that through bad lab practice they could have cross-contaminated their evidence. Until we know they took appropriate measures to stop that, we can't know for sure.
However, this is a very, very real possibility. Kosminski was a leading suspect at the time, has long been since, was named the most likely by FBI profilers and (as kvalidir says), the murders stopped after he was committed. It's entirely possible that the Ripper case has now been solved.